Ch.4 - The Study of Chemical Reactions

Wade9th EditionOrganic ChemistryISBN: 9780135213728Not the one you use?Change textbook

Wade 9th Edition

Ch.4 - The Study of Chemical Reactions

Problem 5b

Chapter 4, Problem 5b

The following reaction has a value of ΔG° = –2.1 kJ/mol (–0.50 kcal/mol).
CH₃Br + H₂S ⇌ CH₃SH + HBr
b. Starting with a 1 M solution of CH3Br and H2S, calculate the final concentrations of all four species at equilibrium.

Verified step by step guidance

Step 1: Write the equilibrium constant expression (K) for the reaction. The reaction is CH3Br + H2S ⇌ CH3SH + HBr. The equilibrium constant expression is:

K = \frac{[CH 3_{SH}] [HBr]}{[CH 3_{Br}] [H 2_{S}]}

Step 2: Use the relationship between ΔG and K to calculate the equilibrium constant. The formula is:

ΔG = - RT ln K

, where ΔG is the Gibbs free energy change (-2.1 kJ/mol), R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin (assume 298 K unless otherwise specified). Rearrange the equation to solve for K:

K = e^{\frac{ΔG}{-RT}}

Step 3: Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of all species. Initially, [CH3Br] = 1 M, [H2S] = 1 M, and [CH3SH] = [HBr] = 0 M. Define the change in concentration of CH3Br and H2S as -x, and the change in concentration of CH3SH and HBr as +x.

Step 4: Express the equilibrium concentrations in terms of x. At equilibrium, [CH3Br] = 1 - x, [H2S] = 1 - x, [CH3SH] = x, and [HBr] = x. Substitute these expressions into the equilibrium constant expression:

K = \frac{x x}{(1 - x) (1 - x)}

Step 5: Solve for x using the value of K calculated in Step 2. This will involve substituting the value of K into the equation and solving the quadratic equation for x. Once x is determined, use it to calculate the equilibrium concentrations of all species: [CH3Br] = 1 - x, [H2S] = 1 - x, [CH3SH] = x, and [HBr] = x.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

11m

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that indicates the spontaneity of a reaction. A negative ΔG value, such as -2.1 kJ/mol, suggests that the reaction is exergonic and will proceed spontaneously towards the products under standard conditions. Understanding ΔG helps predict the direction of the reaction and the extent to which reactants will convert to products at equilibrium.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of concentrations of products to reactants at equilibrium for a reversible reaction. It is derived from the Gibbs Free Energy change, where a negative ΔG corresponds to a K value greater than 1, indicating that products are favored. Calculating K is essential for determining the final concentrations of species in the reaction at equilibrium.

ICE Table (Initial, Change, Equilibrium)

An ICE table is a systematic way to track the concentrations of reactants and products during a chemical reaction as it progresses towards equilibrium. It includes initial concentrations, the changes in concentration as the reaction proceeds, and the equilibrium concentrations. Using an ICE table allows for the calculation of the final concentrations of all species involved in the reaction, based on the stoichiometry and equilibrium constant.

Recommended video:

Guided course

01:46

Why we use pKa instead of pH.

Related Practice

Textbook Question

Use the bond-dissociation enthalpies in Table 4-2 (page 167) to calculate the heats of reaction for the two possible first propagation steps in the chlorination of isobutane. Use this information to draw a reaction-energy diagram like Figure 4-8, comparing the activation energies for formation of the two radicals.

1047

views

Textbook Question

When ethene is mixed with hydrogen in the presence of a platinum catalyst, hydrogen adds across the double bond to form ethane. At room temperature, the reaction goes to completion. Predict the signs of ΔH° and ΔS° for this reaction. Explain these signs in terms of bonding and freedom of motion.

3051

views

Textbook Question

Under base-catalyzed conditions, two molecules of acetone can condense to form diacetone alcohol. At room temperature (25 °C), about 5% of the acetone is converted to diacetone alcohol. Determine the value of ΔG° for this reaction.

1269

views

Textbook Question

Free-radical chlorination of hexane gives very poor yields of 1-chlorohexane, while cyclohexane can be converted to chlorocyclohexane in good yield.

a. How do you account for this difference?

b. What ratio of reactants (cyclohexane and chlorine) would you use for the synthesis of chlorocyclohexane?

2423

views

Textbook Question

The following reaction has a value of ΔG° = –2.1 kJ/mol (–0.50 kcal/mol).

CH₃Br + H₂S ⇌ CH₃SH + HBr

a. Calculate K_eq at room temperature (25 °C) for this reaction as written.